Download Viscosity

MECH 225 Engineering Science 2
1.4 Viscosity
Viscosity is a measure of the effect of friction in fluid flow.
Why does friction exist in fluid flow?
higher velocity
τ
momentum transfer
τ
Flow Direction
τ0
τ0
zero velocity no-slip condition
•
molecular collisions – the molecules of the fluid bump into each other,
slowing down their motion
•
momentum transfer from higher momentum to lower - momentum is mass
times velocity, mu. During a collision, momentum will be transferred.
•
measured by shear stress, τ, which is the tangential force divided by the
area
What fluid parameters does the shear stress depend on?
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•
In solids, the shear stress, τ, is proportional to the applied force.
•
In liquids, the shear stress depends on
relative movement between layers of
fluid.
•
If the velocity is constant across the
flow field, then there is no friction –
often assumed to be the case away
from a solid wall.
•
In fluids, τ depends on
-
the rate of change of velocity with
distance across the stream
-
fluid properties
y
u
du
dy
du/dy is the rate of change of velocity with distance from the surface, where u
is the flow velocity, and y is the distance from the plate, across the flow.
Near the surface, the rate of change of velocity is high, but further away from
the plate the velocity changes more slowly, and may become constant, so
du/dy gets smaller.
The shear stress is proportional to the rate of change of velocity, also called
du
the velocity gradient. We can write this as: τ ∝
dy
So near the surface, the shear stress is high, while on moving further into the
stream the shear stress gets smaller.
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Since τ ∝
du
we can also write
dy
τ = a constant * du/dy
The constant is called the dynamic viscosity of the fluid and is given the
Greek symbol, µ, ‘mu’. Thus:
τ=µ
du
dy
(Newton’s equation)
Viscosity is often associated with density, ρ, so a useful parameter is the
kinematic viscosity, given the symbol ν ‘nu’, where
ν=
µ
ρ
What are the units of dynamic viscosity and kinematic viscosity?
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Units of viscosity
Dynamic viscosity
µ
N s m-2 or Pa s or kg m-1 s-1
Kinematic viscosity
ν
m2 s-1
Typical values of µ at 15°C (288 K):
Air
Water
Diesel oil
Olive oil
18 x 10-6 Pa s
1.139 x 10-3 Pa s
4.5 x 10-3 Pa s
106.1x 10-3 Pa s
Viscosity is strongly dependent on temperature: for liquids, the viscosity
reduces as the temperature is raised, while for gases, the viscosity is
approximately proportional to the square root of the absolute temperature, and
therefore increases with temperature.
Measurement of Viscosity
There are 3 main types of viscometer:
•
measures the time taken for a fixed volume of fluid to pass through a
capillary tube e.g. Redwood viscometer
•
the falling sphere method, good for highly viscous fluids;
•
rotary devices
Further reading:
Bacon and Stephens, Fluid Mechanics for Technicians 3/4
Chapter 6
Bacon and Stephens, Mechanical Technology
31.2
Massey, Mechanics of fluids
1.5, 6.5
White, Fluid Mechanics
1.7
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